1. Technical Field
The invention relates to a method and device for determining by photoelasticity the distribution of a deformation or stress field in a work piece subjected to loads.
2. Prior Art
Photoelasticimetry is a method based on birefringence, due to the anisotropy created by deformations in work pieces or coatings made from a normally mono-refringent transparent material. For carrying out the method, two-dimensional images are formed of a test piece or model representing a work piece, subjected to the loads whose effect is to be studied. Images are formed under conditions such that there are interference fringes between ordinary and extraordinary rays, which fringes represent the distribution of the shearing stresses.
The measurements using photoelasticity make available images containing the full information required for determining the internal deformations or stresses of a work piece. However, the method is generally used for obtaining qualitative information only, particularly for determining the maximum shearing stress lines. For this application, the photoelasticimetry processes provide very rapidly an overall display of the shearing field from which zones of maximum shearing may be obtained, with low investment and implementation costs.
A reason why the measurement of photoelasticimetry is little used for determining the distribution of stresses along selected lines through the test piece is that it does not give access directly to the quantitative information which is of interest for the engineer, i.e. the the values of the principal stresses and the orientation thereof.
The image of the test piece studied obtained by directing a light beam successively through a polarizer, the test-piece and an analyser (generally parallel to the polarizer or crossed therewith) has:
constant color bands, called isochromatic fringes or lines, which correspond to the locii having the same difference .delta. of the light paths of the two types or rays, and
black lines, called isoclinic fringes or isoclinals, which are locii of the points where the main stresses in the test piece have a predetermined direction depending on the mutual angular position of the polarizer and analyzer.
Images showing ones or others of the two line arrays may be obtained by using the fact that the isochromatic lines are independent of the polarization direction whereas a modification of this direction changes the isoclinals. Conventionally, the isoclinals are eliminated by illuminating the test piece with circularly polarized light and the isochromatic lines are independent of the polarization direction whereas a modification of this direction changes the isoclinals. Conventionally, the isoclinals are eliminated by illuminating the test piece with circularly polarized light and the isochromatics are spread out by illuminating the test piece with white light to enhance the isoclinals, which are independent of the wave length.
At any given point of the test-piece, the ellipsoid of the deformations (and of the stresses in the case of a test-piece made of isotropic material, which alone will be considered hereafter) and the ellipsoid of the optical indices have the same principal axes. In the cross-section of the two ellipsoids by a wave plane containing a principal plane, the directions of the principal stresses .sigma.I and .sigma.II coincide with those of the principal optical indices N1 and N2. As long as the index variation remains small, there exists a relationship of the form: EQU .delta.=C e(.sigma.I-.sigma.II) (1)
where .delta. is the phase difference, e is the thickness of material passed through and C is a constant value called photoelasticity constant.
Examination of the isochromatic lines makes it possible to determine .sigma.I-.sigma.II at each point and that of the isoclinals for several polarization directions makes it possible to determine the angle .alpha. of the direction of one of the principal stresses with a reference direction (FIG. 1) or the angle .beta. with the polarization direction.
But the engineer is generally interested in measuring .sigma.I, .sigma.II and .alpha. at a number of points.
A first approach for obtaining the values of .sigma.l and .sigma.II at each point consists in making other measurements on the test-piece, using a method giving an indication about .sigma.I+.sigma.II at each point, such as thermoelasticity. But this solution complicates and extends the duration of the measurements and requires expensive apparatus.
The invention starts from an entirely different approach. It uses the fact that, if part at least of the test-piece is available and the conditions at the limits are known, it becomes possible to integrate the well-known equilibrium equation: EQU (.delta..sigma..sub.x /.delta.x)+(.delta..tau..sub.y /.delta.y)=0 (2)
Thus the relationships required for obtaining the main stresses are available.
But computation is very heavy and difficult to carry out manually. In practice, the measurement of photoelasticity is consequently used at the present time as a tool for searching for the points of maximum shearing.